OR Code No.: NR- 411354 IV B.Tech -I Semester Supplementary Examinations, November-2004 ADAPTIVE CONTROL SYSTEMS (Electronics and Control Engineering) Marks: 70 Answer any FIVE questions. All questions carry equal marks. ---

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Time: 3 hours

With help of block diagram explain the adaptive control system. Explain learning in adaptive systems.

2.a)

Explain the direct self tuning regulator algorithm for Non-minimum phase systems.

b)

Consider the process

G ( s) 

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1.a) b)

1 , where p is an unknown parameter. s( s  p)

Determine suitable adaptive controller that can give the closed control system

2 Gm ( s )  2 based on stability theory. s  2 s   2

Draw the block diagram of a model reference adaptive system and explain the adjustment of system parameters to satisfy the selected error criteria.

4.

Consider the system G(s) = G1(s) G2(s) b c Where G1 ( s )  , G2 ( s )  sa sd where a and b are unknown parameters and c and d are known. Construct discrete-time indirect self-tuning algorithms for the partially known system.

5.

Consider the model y(t) = a + b.t +e(t) t=1,2,3, . . . . where {e(t)} is a sequence of uncorrelated N(0,1) random variables. Determine the least-squares estimate of the parameters a and b. Also determine the covariance of the estimate. Discuss the behavior of the covariance as the number of estimates increases.

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3.

Compare the explicit and implicit self-tuning regulators. Explain the pole placement of self-tuning regulators.

7.

Consider an MRAS for adjustment of a feedforward gain based on the MIT rule. Let the command signal be uc  a1 sin 1t  a2 sin  2t and assume that the process 1 has the transfer function G ( s )  . Derive conditions for the closed-loop s  13 system to be stable. (Contd…2)

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6.a) b)

Code No.: 411354

OR

Write short notes on the following: (a) Hyper stability design (b) Marx system. (c) Learning in adaptive systems.

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